A disc of mass 10 g is kept floating horizontally by throwing 10 marbles per second against it from below. If the mass of each marble is 5 g . What will be velocity with which the marble are striking the disc? Assume that, the marble strikes the disc normally and rebound downwards with the same speed.

Three blocks of masses $$m_1, m_2$$ and $$m_3$$ are connected by massless strings, as shown, on a frictionless table. They are pulled with a force, $$T_3=40 \mathrm{~N}$$. If $$m_1=10 \mathrm{~kg}, m_2=8 \mathrm{~kg}$$ and $$m_3=2 \mathrm{~kg}$$, the tension $$T_2$$ will be

The system is pushed by a force $$F$$ as shown in figure. All surfaces are smooth except between $$B$$ and $$C$$. Friction coefficient between $$B$$ and $$C$$ is $$\mu$$. Minimum value of $$F$$ to prevent block $$B$$ from downward slipping is